diff --git a/src/buildHTML.js b/src/buildHTML.js
index 129f6877..ddcbd19c 100644
--- a/src/buildHTML.js
+++ b/src/buildHTML.js
@@ -762,20 +762,57 @@ groupTypes.spacing = function(group, options) {
     }
 };
 
-groupTypes.llap = function(group, options) {
-    const inner = makeSpan(
-        ["inner"], [buildGroup(group.value.body, options)]);
+groupTypes.lap = function(group, options) {
+    // mathllap, mathrlap, mathclap
+    let inner;
+    if (group.value.alignment === "clap") {
+        // ref: https://www.math.lsu.edu/~aperlis/publications/mathclap/
+        inner = makeSpan([], [buildGroup(group.value.body, options)]);
+        // wrap, since CSS will center a .clap > .inner > span
+        inner = makeSpan(["inner"], [inner], options);
+    } else {
+        inner = makeSpan(
+            ["inner"], [buildGroup(group.value.body, options)]);
+    }
     const fix = makeSpan(["fix"], []);
     return makeSpan(
-        ["mord", "llap"], [inner, fix], options);
+        ["mord", group.value.alignment], [inner, fix], options);
 };
 
-groupTypes.rlap = function(group, options) {
-    const inner = makeSpan(
-        ["inner"], [buildGroup(group.value.body, options)]);
-    const fix = makeSpan(["fix"], []);
-    return makeSpan(
-        ["mord", "rlap"], [inner, fix], options);
+groupTypes.smash = function(group, options) {
+    const node = makeSpan(["mord"], [buildGroup(group.value.body, options)]);
+
+    if (!group.value.smashHeight && !group.value.smashDepth) {
+        return node;
+    }
+
+    if (group.value.smashHeight) {
+        node.height = 0;
+        // In order to influence makeVList, we have to reset the children.
+        if (node.children) {
+            for (let i = 0; i < node.children.length; i++) {
+                node.children[i].height = 0;
+            }
+        }
+    }
+
+    if (group.value.smashDepth) {
+        node.depth = 0;
+        if (node.children) {
+            for (let i = 0; i < node.children.length; i++) {
+                node.children[i].depth = 0;
+            }
+        }
+    }
+
+    // At this point, we've reset the TeX-like height and depth values.
+    // But the span still has an HTML line height.
+    // makeVList applies "display: table-cell", which prevents the browser
+    // from acting on that line height. So we'll call makeVList now.
+
+    return buildCommon.makeVList([
+        {type: "elem", elem: node},
+    ], "firstBaseline", null, options);
 };
 
 groupTypes.op = function(group, options) {
@@ -1698,6 +1735,34 @@ groupTypes.phantom = function(group, options) {
     return new buildCommon.makeFragment(elements);
 };
 
+groupTypes.hphantom = function(group, options) {
+    let node = makeSpan(
+        [], [buildGroup(group.value.body, options.withPhantom())]);
+    node.height = 0;
+    node.depth = 0;
+    if (node.children) {
+        for (let i = 0; i < node.children.length; i++) {
+            node.children[i].height = 0;
+            node.children[i].depth = 0;
+        }
+    }
+
+    // See smash for comment re: use of makeVList
+    node = buildCommon.makeVList([
+        {type: "elem", elem: node},
+    ], "firstBaseline", null, options);
+
+    return node;
+};
+
+groupTypes.vphantom = function(group, options) {
+    const inner = makeSpan(
+        ["inner"], [buildGroup(group.value.body, options.withPhantom())]);
+    const fix = makeSpan(["fix"], []);
+    return makeSpan(
+        ["mord", "rlap"], [inner, fix], options);
+};
+
 groupTypes.mclass = function(group, options) {
     const elements = buildExpression(group.value.value, options, true);
 
diff --git a/src/buildMathML.js b/src/buildMathML.js
index 9979397d..79e4aa78 100644
--- a/src/buildMathML.js
+++ b/src/buildMathML.js
@@ -621,21 +621,31 @@ groupTypes.kern = function(group) {
     return node;
 };
 
-groupTypes.llap = function(group, options) {
+groupTypes.lap = function(group, options) {
+    // mathllap, mathrlap, mathclap
     const node = new mathMLTree.MathNode(
         "mpadded", [buildGroup(group.value.body, options)]);
 
-    node.setAttribute("lspace", "-1width");
+    if (group.value.alignment !== "rlap")    {
+        const offset = (group.value.alignment === "llap" ? "-1" : "-0.5");
+        node.setAttribute("lspace", offset + "width");
+    }
     node.setAttribute("width", "0px");
 
     return node;
 };
 
-groupTypes.rlap = function(group, options) {
+groupTypes.smash = function(group, options) {
     const node = new mathMLTree.MathNode(
         "mpadded", [buildGroup(group.value.body, options)]);
 
-    node.setAttribute("width", "0px");
+    if (group.value.smashHeight) {
+        node.setAttribute("height", "0px");
+    }
+
+    if (group.value.smashDepth) {
+        node.setAttribute("depth", "0px");
+    }
 
     return node;
 };
@@ -645,6 +655,20 @@ groupTypes.phantom = function(group, options) {
     return new mathMLTree.MathNode("mphantom", inner);
 };
 
+groupTypes.hphantom = function(group, options) {
+    const inner = buildExpression(group.value.value, options);
+    const node = new mathMLTree.MathNode("mphantom", inner);
+    node.setAttribute("height", "0px");
+    return node;
+};
+
+groupTypes.vphantom = function(group, options) {
+    const inner = buildExpression(group.value.value, options);
+    const node = new mathMLTree.MathNode("mphantom", inner);
+    node.setAttribute("width", "0px");
+    return node;
+};
+
 groupTypes.mclass = function(group, options) {
     const inner = buildExpression(group.value.value, options);
     return new mathMLTree.MathNode("mstyle", inner);
diff --git a/src/functions.js b/src/functions.js
index 6d09a82d..5db624c2 100644
--- a/src/functions.js
+++ b/src/functions.js
@@ -234,13 +234,14 @@ defineFunction("\\KaTeX", {
     };
 });
 
-defineFunction("\\phantom", {
+defineFunction(["\\phantom", "\\hphantom", "\\vphantom"], {
     numArgs: 1,
 }, function(context, args) {
     const body = args[0];
     return {
-        type: "phantom",
+        type: context.funcName.slice(1),
         value: ordargument(body),
+        body: body,
     };
 });
 
@@ -516,18 +517,59 @@ defineFunction([
     };
 });
 
-// Left and right overlap functions
-defineFunction(["\\llap", "\\rlap"], {
+// Horizontal overlap functions
+defineFunction(["\\mathllap", "\\mathrlap", "\\mathclap"], {
     numArgs: 1,
     allowedInText: true,
 }, function(context, args) {
     const body = args[0];
     return {
-        type: context.funcName.slice(1),
+        type: "lap",
+        alignment: context.funcName.slice(5),
         body: body,
     };
 });
 
+// smash, with optional [tb], as in AMS
+defineFunction("\\smash", {
+    numArgs: 1,
+    numOptionalArgs: 1,
+    allowedInText: true,
+}, function(context, args) {
+    let smashHeight = false;
+    let smashDepth = false;
+    const tbArg = args[0];
+    if (tbArg) {
+        // Optional [tb] argument is engaged.
+        // ref: amsmath: \renewcommand{\smash}[1][tb]{%
+        //               def\mb@t{\ht}\def\mb@b{\dp}\def\mb@tb{\ht\z@\z@\dp}%
+        let letter = "";
+        for (let i = 0; i < tbArg.value.length; ++i) {
+            letter = tbArg.value[i].value;
+            if (letter === "t") {
+                smashHeight = true;
+            } else if (letter === "b") {
+                smashDepth = true;
+            } else {
+                smashHeight = false;
+                smashDepth = false;
+                break;
+            }
+        }
+    } else {
+        smashHeight = true;
+        smashDepth = true;
+    }
+
+    const body = args[1];
+    return {
+        type: "smash",
+        body: body,
+        smashHeight: smashHeight,
+        smashDepth: smashDepth,
+    };
+});
+
 // Delimiter functions
 const checkDelimiter = function(delim, context) {
     if (utils.contains(delimiters, delim.value)) {
diff --git a/src/macros.js b/src/macros.js
index 9d172e85..63ef710e 100644
--- a/src/macros.js
+++ b/src/macros.js
@@ -19,6 +19,11 @@ defineMacro("\\endgroup", "}");
 // (In TeX, the mu unit works only with \mkern.)
 defineMacro("\\mkern", "\\kern");
 
+// \llap and \rlap render their contents in text mode
+defineMacro("\\llap", "\\mathllap{\\textrm{#1}}");
+defineMacro("\\rlap", "\\mathrlap{\\textrm{#1}}");
+defineMacro("\\clap", "\\mathclap{\\textrm{#1}}");
+
 //////////////////////////////////////////////////////////////////////
 // amsmath.sty
 
@@ -38,6 +43,19 @@ defineMacro("\\iff", "\\;\\Longleftrightarrow\\;");
 defineMacro("\\implies", "\\;\\Longrightarrow\\;");
 defineMacro("\\impliedby", "\\;\\Longleftarrow\\;");
 
+// http://texdoc.net/texmf-dist/doc/latex/amsmath/amsmath.pdf
+defineMacro("\\thinspace", "\\,");    //   \let\thinspace\,
+defineMacro("\\medspace", "\\:");     //   \let\medspace\:
+defineMacro("\\thickspace", "\\;");   //   \let\thickspace\;
+
+//////////////////////////////////////////////////////////////////////
+// LaTeX source2e
+
+// \DeclareRobustCommand\hspace{\@ifstar\@hspacer\@hspace}
+// \def\@hspace#1{\hskip  #1\relax}
+// KaTeX doesn't do line breaks, so \hspace is the same as \kern
+defineMacro("\\hspace", "\\kern{#1}");
+
 //////////////////////////////////////////////////////////////////////
 // mathtools.sty
 
diff --git a/static/katex.less b/static/katex.less
index 1a97a23e..b009b7bf 100644
--- a/static/katex.less
+++ b/static/katex.less
@@ -350,7 +350,8 @@
     }
 
     .llap,
-    .rlap {
+    .rlap,
+    .clap {
         width: 0;
         position: relative;
 
@@ -367,10 +368,16 @@
         right: 0;
     }
 
-    .rlap > .inner {
+    .rlap > .inner,
+    .clap > .inner {
         left: 0;
     }
 
+    .clap > .inner  > span {
+        margin-left: -50%;
+        margin-right: 50%;
+    }
+
     .katex-logo {
         .a {
             font-size: 0.75em;
diff --git a/test/katex-spec.js b/test/katex-spec.js
index 06e78f81..5f217990 100644
--- a/test/katex-spec.js
+++ b/test/katex-spec.js
@@ -1253,15 +1253,15 @@ describe("A TeX-compliant parser", function() {
             "\\frac x \\frac y z",
             "\\frac \\sqrt x y",
             "\\frac x \\sqrt y",
-            "\\frac \\llap x y",
-            "\\frac x \\llap y",
+            "\\frac \\mathllap x y",
+            "\\frac x \\mathllap y",
             // This actually doesn't work in real TeX, but it is suprisingly
             // hard to get this to correctly work. So, we take hit of very small
             // amounts of non-compatiblity in order for the rest of the tests to
             // work
             // "\\llap \\frac x y",
-            "\\llap \\llap x",
-            "\\sqrt \\llap x",
+            "\\mathllap \\mathllap x",
+            "\\sqrt \\mathllap x",
         ];
 
         for (let i = 0; i < badArguments.length; i++) {
@@ -1275,11 +1275,11 @@ describe("A TeX-compliant parser", function() {
             "\\frac x {\\frac y z}",
             "\\frac {\\sqrt x} y",
             "\\frac x {\\sqrt y}",
-            "\\frac {\\llap x} y",
-            "\\frac x {\\llap y}",
-            "\\llap {\\frac x y}",
-            "\\llap {\\llap x}",
-            "\\sqrt {\\llap x}",
+            "\\frac {\\mathllap x} y",
+            "\\frac x {\\mathllap y}",
+            "\\mathllap {\\frac x y}",
+            "\\mathllap {\\mathllap x}",
+            "\\sqrt {\\mathllap x}",
         ];
 
         for (let i = 0; i < goodArguments.length; i++) {
@@ -1290,9 +1290,9 @@ describe("A TeX-compliant parser", function() {
     it("should fail when sup/subscripts require arguments", function() {
         const badSupSubscripts = [
             "x^\\sqrt x",
-            "x^\\llap x",
+            "x^\\mathllap x",
             "x_\\sqrt x",
-            "x_\\llap x",
+            "x_\\mathllap x",
         ];
 
         for (let i = 0; i < badSupSubscripts.length; i++) {
@@ -1303,9 +1303,9 @@ describe("A TeX-compliant parser", function() {
     it("should work when sup/subscripts arguments have braces", function() {
         const goodSupSubscripts = [
             "x^{\\sqrt x}",
-            "x^{\\llap x}",
+            "x^{\\mathllap x}",
             "x_{\\sqrt x}",
-            "x_{\\llap x}",
+            "x_{\\mathllap x}",
         ];
 
         for (let i = 0; i < goodSupSubscripts.length; i++) {
@@ -1341,7 +1341,7 @@ describe("A TeX-compliant parser", function() {
         const badLeftArguments = [
             "\\frac \\left( x \\right) y",
             "\\frac x \\left( y \\right)",
-            "\\llap \\left( x \\right)",
+            "\\mathllap \\left( x \\right)",
             "\\sqrt \\left( x \\right)",
             "x^\\left( x \\right)",
         ];
@@ -1355,7 +1355,7 @@ describe("A TeX-compliant parser", function() {
         const goodLeftArguments = [
             "\\frac {\\left( x \\right)} y",
             "\\frac x {\\left( y \\right)}",
-            "\\llap {\\left( x \\right)}",
+            "\\mathllap {\\left( x \\right)}",
             "\\sqrt {\\left( x \\right)}",
             "x^{\\left( x \\right)}",
         ];
@@ -2088,6 +2088,10 @@ describe("A phantom parser", function() {
         expect("\\phantom{x^2}").toParse();
         expect("\\phantom{x}^2").toParse();
         expect("\\phantom x").toParse();
+        expect("\\hphantom{x}").toParse();
+        expect("\\hphantom{x^2}").toParse();
+        expect("\\hphantom{x}^2").toParse();
+        expect("\\hphantom x").toParse();
     });
 
     it("should build a phantom node", function() {
@@ -2104,6 +2108,11 @@ describe("A phantom builder", function() {
         expect("\\phantom{x^2}").toBuild();
         expect("\\phantom{x}^2").toBuild();
         expect("\\phantom x").toBuild();
+
+        expect("\\hphantom{x}").toBuild();
+        expect("\\hphantom{x^2}").toBuild();
+        expect("\\hphantom{x}^2").toBuild();
+        expect("\\hphantom x").toBuild();
     });
 
     it("should make the children transparent", function() {
@@ -2121,6 +2130,45 @@ describe("A phantom builder", function() {
     });
 });
 
+describe("A smash parser", function() {
+    it("should not fail", function() {
+        expect("\\smash{x}").toParse();
+        expect("\\smash{x^2}").toParse();
+        expect("\\smash{x}^2").toParse();
+        expect("\\smash x").toParse();
+
+        expect("\\smash[b]{x}").toParse();
+        expect("\\smash[b]{x^2}").toParse();
+        expect("\\smash[b]{x}^2").toParse();
+        expect("\\smash[b] x").toParse();
+
+        expect("\\smash[]{x}").toParse();
+        expect("\\smash[]{x^2}").toParse();
+        expect("\\smash[]{x}^2").toParse();
+        expect("\\smash[] x").toParse();
+    });
+
+    it("should build a smash node", function() {
+        const parse = getParsed("\\smash{x}")[0];
+
+        expect(parse.type).toEqual("smash");
+    });
+});
+
+describe("A smash builder", function() {
+    it("should not fail", function() {
+        expect("\\smash{x}").toBuild();
+        expect("\\smash{x^2}").toBuild();
+        expect("\\smash{x}^2").toBuild();
+        expect("\\smash x").toBuild();
+
+        expect("\\smash[b]{x}").toBuild();
+        expect("\\smash[b]{x^2}").toBuild();
+        expect("\\smash[b]{x}^2").toBuild();
+        expect("\\smash[b] x").toBuild();
+    });
+});
+
 describe("A parser error", function() {
     it("should report the position of an error", function() {
         try {
diff --git a/test/screenshotter/images/Lap-chrome.png b/test/screenshotter/images/Lap-chrome.png
index 5e5d36bd..a8d14b29 100644
Binary files a/test/screenshotter/images/Lap-chrome.png and b/test/screenshotter/images/Lap-chrome.png differ
diff --git a/test/screenshotter/images/Lap-firefox.png b/test/screenshotter/images/Lap-firefox.png
index 6b7ae932..17c982d8 100644
Binary files a/test/screenshotter/images/Lap-firefox.png and b/test/screenshotter/images/Lap-firefox.png differ
diff --git a/test/screenshotter/images/Phantom-chrome.png b/test/screenshotter/images/Phantom-chrome.png
index da7a6d68..9f1db3f6 100644
Binary files a/test/screenshotter/images/Phantom-chrome.png and b/test/screenshotter/images/Phantom-chrome.png differ
diff --git a/test/screenshotter/images/Phantom-firefox.png b/test/screenshotter/images/Phantom-firefox.png
index 730f9a82..e9f70656 100644
Binary files a/test/screenshotter/images/Phantom-firefox.png and b/test/screenshotter/images/Phantom-firefox.png differ
diff --git a/test/screenshotter/images/Smash-chrome.png b/test/screenshotter/images/Smash-chrome.png
new file mode 100644
index 00000000..8d0a0551
Binary files /dev/null and b/test/screenshotter/images/Smash-chrome.png differ
diff --git a/test/screenshotter/images/Smash-firefox.png b/test/screenshotter/images/Smash-firefox.png
new file mode 100644
index 00000000..2e58032b
Binary files /dev/null and b/test/screenshotter/images/Smash-firefox.png differ
diff --git a/test/screenshotter/ss_data.yaml b/test/screenshotter/ss_data.yaml
index 62a52c1d..1b7abf48 100644
--- a/test/screenshotter/ss_data.yaml
+++ b/test/screenshotter/ss_data.yaml
@@ -107,7 +107,7 @@ KaTeX: \KaTeX
 Kern:
     tex: \frac{a\kern{1em}b}{c}a\kern{1em}b\kern{1ex}c\kern{-0.25em}d
     nolatex: LaTeX fails to typeset this, “Missing number, treated as zero.”
-Lap: ab\llap{f}cd\rlap{g}h
+Lap: ab\mathllap{f}cd\mathrlap{g}hij\mathclap{k}lm \; ab\llap{f}cd\rlap{g}hij\clap{k}lm
 LargeRuleNumerator: \frac{\textcolor{blue}{\rule{1em}{2em}}}{x}
 LeftRight: \left( x^2 \right) \left\{ x^{x^{x^{x^x}}} \right.
 LeftRightListStyling: a+\left(x+y\right)-x
@@ -178,7 +178,7 @@ OverUnderset: |
     a+b+c+d\overset{b+c=0}\longrightarrow a+d\\
     \overset { x = y } { \sqrt { a b } }
     \end{array}
-Phantom: \dfrac{1+\phantom{x^{\blue{2}}} = x}{1+x^{\blue{2}} = x}
+Phantom: \dfrac{1+\phantom{x^{\blue{2}}} = x}{1+x^{\blue{2}} = x} \left(\vphantom{\int_t} zzz \right) \left( X \hphantom{\frac{\frac X X}{X}} \right)
 PrimeSpacing: f'+f_2'+f^{f'}
 PrimeSuper: x'^2+x'''^2+x'^2_3+x_3'^2
 RelativeUnits: |
@@ -190,7 +190,7 @@ RelativeUnits: |
         \rule{1em}{1em}^{\rule{1em}{1em}}\rule{18mu}{18mu}^{\rule{18mu}{18mu}} &
         {\footnotesize\rule{1em}{1em}^{\rule{1em}{1em}}\rule{18mu}{18mu}^{\rule{18mu}{18mu}}}
     \end{array}
-RlapBug: \frac{\rlap{x}}{2}
+RlapBug: \frac{\mathrlap{x}}{2}
 Rule: \rule{1em}{0.5em}\rule{1ex}{2ex}\rule{1em}{1ex}\rule{1em}{0.431ex}
 SizingBaseline:
     tex: '{\tiny a+b}a+b{\Huge a+b}'
@@ -198,6 +198,7 @@ SizingBaseline:
     post: M
 Sizing: |
     {\Huge x}{\LARGE y}{\normalsize z}{\scriptsize w}
+Smash: \left( X^{\smash 2} \right) \sqrt{\smash[b]{y}}
 Spacing: ^3+[-1][1-1]1=1(=1)\lvert a\rvert~b
 Sqrt: |
     \sqrt{\sqrt{\sqrt{x}}}_{\sqrt{\sqrt{x}}}^{\sqrt{\sqrt{\sqrt{x}}}